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Finding 3 × 3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

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Abstract.

We show that any 3-component octonionic vector which is purely imaginary, but not quaternionic, is an eigenvector of a 6-parameter family of Hermitian octonionic matrices, with imaginary eigenvalue equal to the associator of its elements.

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Authors and Affiliations

  1. Department of Science and Mathematics Education, Oregon State University, Corvallis, OR, 97331, USA

    Henry Gillow-Wiles

  2. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

    Tevian Dray

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  1. Henry Gillow-Wiles
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  2. Tevian Dray
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Correspondence to Tevian Dray.

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Gillow-Wiles, H., Dray, T. Finding 3 × 3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues. AACA 20, 247–254 (2010). https://doi.org/10.1007/s00006-010-0201-4

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  • DOI: https://doi.org/10.1007/s00006-010-0201-4

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